For which, may I remind, you must either abandon Noether or you must abandon Einstein(*)

(*) Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K. —Albert Einstein: The foundation of the general theory of relativity, Section A, §1

Oh, and the total force on the mirrors (assume attached to one another via a vertical truss) is 4 P/c, where P is the power of the beam. By symmetry, that's the total force integrated over the bend. Net force = 0.

Photons are in a different frame of reference. The above system should move to the left.

The above system as well as EmDrive is like a cavity with an externally attached pendulum. The pendulum's ball (represents light wave or microwave) bounces in it. And moves the light/MW cavity to the side where it bounces the most.

It will not "move" to the left (or rather you should say "thrust to the left", or equivalently "accelerate to the left" as velocity is always relative while acceleration can be defined in absolute, relative to an inertial test particle). Anyway, it will not, as deltaMass says.

If playing around with curved trajectories of momentum carriers were a way to cheat like that on momentum conservation, it would be long ago mechanical devices such as Dean drives would have been shown to work reliably to provide propulsion, er, action without reaction. Just imagine a perfect ball, attached to a string to a pivot on a plate, the ball is launched parallel to the plate with given velocity. After a quarter circle trajectory it bounces on the plate and make half circle to bounce again (at point opposite from pivot), half circle up, half circle down and so on. This is similar to your photon bouncing back and forth through your optical fibre bundle. When the ball does its half circle trajectory, the centrifugal force pull on the string. While the bounces give impulse to the left, the pull of the string gives impulse to the right. 0 net average.

Likewise imagine you hold a half pipe and someone throws a bowling bowl through it so that it is exiting back to the launcher, wouldn't you experience quite a recoil ? This would be the same recoil, but opposite (to the right) that the sum of the recoil the launcher experienced first when launching, then when catching back the returning bowl (both to the left) . If each you and the launcher are standing on your own skateboard, after the experiment both will have same momentum but opposite direction (same speed but opposite, assuming same weights). If you and the launcher are standing on the same skateboard, after the experiment not only the skateboard has no velocity (assuming starting from rest) but it is also in same position as before. This is conservation of momentum, and has been experimentally shown with great precision in quite a variety of contexts, and has strong theoretical backing with Noether's theorem relating it to translation invariance of space (basically if reality behaves a certain way at location A, then it behaves the same way at location B, all things and fields being equal there are no special places of reality).

For the same reason the MW cavity shouldn't exert any directional force. But it does. And if so, then probably/maybe a similarly built light cavity with large mirrors on one side and bent optical fiber or small mirror on the other side should produce thrust as well.

The number of light bounces (mirror reflectance) would then represent the photonic thrust multiplication factor similar to Q in EmDrive thrust formula devised by Shawyer. ---

Another issue: why not use Peltier element to cool the superconducting cavity instead of liquid gas? The vehicle will need electric power anyway, so why add heavy liquid hydrogen reservoir? The additional electric energy for Peltier cooling shouldn't require as much mass and space as the hydrogen.It may be economical even for satellites, because the large increase in Q and resulting smaller required input power and smaller engine size would justify additional Peltier module.

Please kindly excuse me if this is an incorrect way of thinking for some reason I am not aware of.

Interesting that breaking CofM means that translational invariance dies, and breaking Einstein's SR core principle means that inertial frame invariance dies. Interesting because you may notice that one is essentially the time derivative of the other. And further that breaking CofE means that time invariance dies.

Perhaps that's a deep observation, but I'm not smart enough to know what it means. All I know is that, for a propellantless propulsor, we are forced to choose between killing off one or the other. If we got creative we could kill off both, maybe!

I'm sure my physics friends down the pub here in Cupertino would simply shrug and say that, since momentum appears not be conserved in the first place, there's ample room for odd statements to be correspondingly made about energy conservation (and I have made them here on this forum).

Perhaps there's an exit route out of this bind via playing off conservation of momentum against conservation of energy. Just a wild thought.

For the same reason the MW cavity shouldn't exert any directional force.

No, it shouldn't. Why the high degree of scepticism. Don't fool yourself, the ratio of people believing this is possible to those believing this is impossible in this thread is not representative of the ratio in the general population of engineers and scientists at large. Sometimes a scientific minority is right and the general consensus is wrong. But often, the consensus is right. Contrary to what we see in movies, the ratio of maverick scientist (in fundamental science) that win at the end is low.

Quote

But it does.

It appears to do, in a few labs. A lot of "3 sigmas" experimental signals (probability of .001 that result is due to a fluke rather than a real effect) in fundamental science prove to be flukes after all, or lose cable, or wrong interpretation, or "look elsewhere effect" (that is, if you look hard enough for something in a big enough variety of ways, you will find it, even if it doesn't exist).

Quote

And if so, then probably/maybe a similarly built light cavity with large mirrors on one side and bent optical fiber or small mirror on the other side should produce thrust as well.

If so, then a lot of things become possible, like pulling on one own shoes to fly above the ground. Einstein protects us ! But looks to me bouncing back vs bending 180° would still make no fundamental difference.

Quote

The number of light bounces (mirror reflectance) would then represent the photonic thrust multiplication factor similar to Q in EmDrive thrust formula devised by Shawyer.

mm

Quote

---

Another issue: why not use Peltier element to cool the superconducting cavity instead of liquid gas? The vehicle will need electric power anyway, so why add heavy liquid hydrogen reservoir? The additional electric energy for Peltier cooling shouldn't require as much mass and space as the hydrogen.It may be economical even for satellites, because the large increase in Q and resulting smaller required input power and smaller engine size would justify additional Peltier module.

Please kindly excuse me if this is an incorrect way of thinking for some reason I am not aware of.

Because Peltier effect can't quite reach cryogenic temperatures, for some thermodynamic reason I forgot. Maybe it changed with recent progress on the subject ? Please inquire : what are the limits of low temp. with Peltier effect, now and tomorrow ? Isn't the Peltier effect still quite low in efficiency ?

Because Peltier effect can't quite reach cryogenic temperatures, for some thermodynamic reason I forgot. Maybe it changed with recent progress on the subject ? Please inquire : what are the limits of low temp. with Peltier effect, now and tomorrow ? Isn't the Peltier effect still quite low in efficiency ?

The Peltier limits are below 100K, which is enough for high-temparature superconductors. The efficiency in such temperature is low, but probably that could be economically viable because of much smaller MW input power and smaller superconducting engine size.

That said, I must sadly admit, that this engine won't probably move in free space. It may move on air cushion though, as in the experiments conducted so far on Earth.

Anyway, if so, then it is at least good for new generation of rotorless helicopters, here on Earth.

Interesting that breaking CofM means that translational invariance dies, and breaking Einstein's SR core principle means that inertial frame invariance dies. Interesting because you may notice that one is essentially the time derivative of the other. And further that breaking CofE means that time invariance dies.

Perhaps that's a deep observation, but I'm not smart enough to know what it means. All I know is that, for a propellantless propulsor, we are forced to choose between killing off one or the other. If we got creative we could kill off both, maybe!

I'm sure my physics friends down the pub here in Cupertino would simply shrug and say that, since momentum appears not be conserved in the first place, there's ample room for odd statements to be correspondingly made about energy conservation (and I have made them here on this forum).

Perhaps there's an exit route out of this bind via playing off conservation of momentum against conservation of energy. Just a wild thought.

Killing CoM is killing CoE if SR still stands.Both leading theories about propellantless devices, White's and Woodward's, can pretend to kill none.White mutable vacuum -> extract both momentum and energy from what is there locallyWoodward Mach effect -> extract both momentum and energy from what is there globallyBut none admit that this gives, in effect, a practically limitless energy generator sitting in a box sitting in deep space, even while this could be argued on potentially sane conservation basis (zenergy comes from somewhere...)

I also have my theory that can pretend to kill no principle and yet allows for a device at 1N/kW, it is not strictly propellantless, it emits particles, namely tachyons, allowing it to give more apparent energy than expanded, as tachyons can be seen as energetic debt. Basically it is sending away at FTL speed the energetic debt of the apparent local CoE breaking so that the accountancy is kept in balance overall. This is my "white paper" on the topic. It is somehow reminiscent of the advanced/retarded waves of Woodward, so I probably can't pretend at complete anteriority on that one, maybe just a minor alternate way of stating the same things.

While they don't like to discuss the theories in terms of locally generable energy from fear of association with "free energy looneys", I'm sure both contenders are convinced that their 1N/kW is stable (not frame/history dependant), and know that they must apparently break CoE, that they can be used as generators of ultra cheap (almost free) energy. What makes me think like that is 1/ It makes a whole lot more sense (bringing back no apparent CoE after the 1N/kW fact is untenable)2/ We have never seen a single time any mention of check of dependency of experimental thrust relative to sidereal time or other "absolute frame" relative to which it may vary (if we are to save apparent CoE at the expanse of SR)

Appears the only compulsory casualty is apparent CoE, not necessarily CoE in itself if one can find a suitable positive energy source (or a negative energy sink) and a mechanism to couple with such source (or sink to get rid of debt).

How the (few) other theories out there deal with the apparent CoE demise ?

Based on the advice from the forum we have reformulated our experimental design . We have been given permission to use one of the vacuum chambers at Cal Poly which can pull about 1mT using a mechanical pump. By mounting everything on a pendulum we can measure a displacement using a reflected laser. I am not experienced with laser measurements and would greatly appreciate any advice for improving this measurement. With a simple setup it seems we will be able to see 100 mN easily, hopefully this is within reason at powers ~1200 W.

We have also been considering using aluminum for the frustum to minimize the mass of the pendulum. This would coincide with Todd's theory that a lower Q in the frustum is more desirable. We could easily implement a symmetric copper resonant cavity to between the magnetron and the frsutum:

1st component: A symmetrical resonator cavity that is optimized to store energy at high Q, and plays no role in thrust. Here, we want to store the lowest order mode that the waveguide can sustain because it has the slowest wave velocity inside the waveguide.

I did some basic solutions for a resonant rectangular chamber and found that to isolate the TE 011 mode at a frequency of 2.4503 GHz we would need a box 7.068 x 7.068 x 12.24 cm. Would we want to match the end of this box to the small end of the frustum?

What should the interface look like?Perhaps we should keep our experiment simple and introduce this complication later...

Also, does anyone know the dimensions of the aluminum cavity being constructed at Eagleworks? I believe the picture posted is missing a dimension required to solve for the others, or maybe my geometry is lacking.

Is this design analogous to the "Modified Aluminum Cavity for TE011 Mode Resonance" previously presented by Paul March? Note, there appears to be two chambers separated by a 1/16" plate (aluminum?). As an avid follower of this thread I have not noticed any comments about this dual chamber design. However, I could be misinterpreting the attached image.

This has been a truly fascinating discussion which has never ceased capturing my attention. I feel fortunate to passively witness. Thank you all, especially the replicators.

-Matthew Trimble

Hopefully we can use EW's dimensions and not have to worry about FEA.

The electrical connections into the chamber will allow the circuit to be kept outside and connected with slack to a magnetron on the pendulum. I am concerned that the magnetron will overheat quickly due to a lack of convection cooling, but maybe we can run shorter tests to compensate.

Any thoughts?

Glad to see everyone still asking questions and presenting ideas! It is quite an amazing discussion and I look forward to contributing some data.

Did you or anyone else ever write an excel spreadsheet to calc Shawyers Design Factor? If so pls link it or if not please consider doing it as your skills there are much better than mine.

Yes I have calculated it, but it is a Mathematica program, not an Excel spreadsheet. I posted (earlier in the thread) comparisons of the measurements vs. predictions using Shawyer's and McCulloch's formulas.

You may want to PM @aero to ask whether he did it with Excel (if my memory is correct @aero also calculated Shawyer's Design Factor, as I recall having exchanges in this forum with him).

And of course, when running your program, you will first check your results vs. Shawyer's published Design Factor results, etc., to make sure that your program is correct.

Mathematica looks interesting but maybe later as I suspect there would be a learning curve.

Is this still your Design Factor equation?

Thanks for your assistance. Most appreciated.

I recognize that equation is my Mathematica-writing, but I need a link to the message where I posted it, in order to remember the context. Too long ago

I did, but the Excel file is not suitable for distribution, having all of my work scattered throughout a 500 line file with little or no embedded explanations. That is, it's un-usable even for me, without considerable time discovering what I intended to do. For example, here is my design factor, Df, equations. I think the variables are: Lo - lengthLg1-diameterLg2-diameterDf = 0.844 Df=S_o*Lo((1/Lg1) - (1/lg2)) where S_o = (1-(Lo^2/(Lg1*Lg2)))^-1 Combining Df = Lo*( 1 - (Lo^2/(Lg1*Lg2)))^-1 *((1/Lg1)-(1/Lg2))

So before turning either your or Aero's equation to Excel and posting it to the Wiki for all replicators to use, wpuld you please give some feedback on which is correct?

From my trying to follow the Shawyer DF equations, it seems your equation which uses Rf imay be correct?

Would appreciate a set of data variables that I can use to verify my excel equation gives the same results as your Mathematica equation.

I checked my formula for Shawyer's Design Factor (Eq. 12 of http://www.emdrive.com/theorypaper9-4.pdf ) and it is correct.(The nomenclature could be better: speedOfLightInMedium instead of c, cavityLength instead of demoCavityLength, frequency instead of rfFrequency etc.)

(Note: Shawyer to my knowledge never wrote his Design Factor formula this way, instead he wrote it as a lengthy series of operations. My formula is identical to his, except that it involves fewer steps to calculate, since I eliminated unnecessary calculations)

To make things easier for you I quickly wrote the calculation on an Excel spreadsheet that I attach below.

You can try different inputs and check the results vs. the calculations I posted here:

Based on the advice from the forum we have reformulated our experimental design . We have been given permission to use one of the vacuum chambers at Cal Poly which can pull about 1mT using a mechanical pump. By mounting everything on a pendulum we can measure a displacement using a reflected laser. I am not experienced with laser measurements and would greatly appreciate any advice for improving this measurement. With a simple setup it seems we will be able to see 100 mN easily, hopefully this is within reason at powers ~1200 W.

We have also been considering using aluminum for the frustum to minimize the mass of the pendulum. This would coincide with Todd's theory that a lower Q in the frustum is more desirable. We could easily implement a symmetric copper resonant cavity to between the magnetron and the frsutum:

1st component: A symmetrical resonator cavity that is optimized to store energy at high Q, and plays no role in thrust. Here, we want to store the lowest order mode that the waveguide can sustain because it has the slowest wave velocity inside the waveguide.

I did some basic solutions for a resonant rectangular chamber and found that to isolate the TE 011 mode at a frequency of 2.4503 GHz we would need a box 7.068 x 7.068 x 12.24 cm. Would we want to match the end of this box to the small end of the frustum?

What should the interface look like?Perhaps we should keep our experiment simple and introduce this complication later...

Also, does anyone know the dimensions of the aluminum cavity being constructed at Eagleworks? I believe the picture posted is missing a dimension required to solve for the others, or maybe my geometry is lacking.

Is this design analogous to the "Modified Aluminum Cavity for TE011 Mode Resonance" previously presented by Paul March? Note, there appears to be two chambers separated by a 1/16" plate (aluminum?). As an avid follower of this thread I have not noticed any comments about this dual chamber design. However, I could be misinterpreting the attached image.

This has been a truly fascinating discussion which has never ceased capturing my attention. I feel fortunate to passively witness. Thank you all, especially the replicators.

-Matthew Trimble

Hopefully we can use EW's dimensions and not have to worry about FEA.

The electrical connections into the chamber will allow the circuit to be kept outside and connected with slack to a magnetron on the pendulum. I am concerned that the magnetron will overheat quickly due to a lack of convection cooling, but maybe we can run shorter tests to compensate.

Any thoughts?

Glad to see everyone still asking questions and presenting ideas! It is quite an amazing discussion and I look forward to contributing some data.

Kurt Zeller

Kurt,

I wish I knew the type of interface to use. I am not an expert in microwave components, but I'm researching as time permits. Also, at 2.4503 GHz, it's going to be pretty large. Did you calculate the wave velocity for that mode?

I was wondering in your testing did you use a smoke stick also called a smoke pencil to check for air flows around the EM Drive in ambient air conditions?

Although a Google search reveals that this has been brought up before, for example here by @aero: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1275034#msg1275034 there is no entry I could find in the threads as to whether any of the research groups actually used smoke to check air flow. Perhaps others can try separate searches either using their memories or using Google (anything but the poorly functioning "Search" button between "Unread Topics" and "Profile" )

Amazing ! Found it after all these years. I have to re-read and re-understand it of course, but check Fig. 1. "The sandwich wave" where you have a section of curved space-time sandwiched between flat. That alone is closer to this situation than anything I've seen so far.

The previous article, Rosen, Joe. "Embedding of Various Relativistic Riemannian Spaces in Pseudo-Euclidean Spaces" contains tables of transforms. That could prove invaluable !

An earlier paper, this time by Bondi, on sandwich waves and plane gravitational waves, that, unlike the other ones, has a PDF with a link :

Plane gravitational waves are here defined to be non-flat solutions of Einstein's empty spacetimefield equations which admit as much symmetry as do plane electromagnetic waves,namely, a 5-parameter group of motions. A general plane-wave metric is written down andthe properties of plane wave space-times are studied in detail. In particular, their characterizationas 'plane' is justified further by the construction of 'sandwich waves' bounded on bothsides by (null) hyperplanes in flat space-time. It is shown that the passing of a sandwich waveproduces a relative acceleration in free test particles, and inferred from this that such wavestransport energy.

Bondi wrote the following regarding the possibility to extract energy from plane gravitational waves (Bondi points out that he had brought this up in 1957):

Quote

As previously pointed out by one of us (Bondi I957), this relative acceleration andconsequent relative velocity prove that gravitational waves transport energy, sinceit is in principle possible, utilizing this effect, to construct a device which will extractenergy from a wave. The simplest such device consists of a stiff rod (the rod need notbe rigid in the technical sense, and the difficulties surrounding the consideration ofrigid bodies in relativity theory are not relevant here) and a bead which slides on therod with some friction. If the rod lies in a suitable direction transverse to thedirection of wave propagation, and if the bead is at rest relative to the rod at aposition well displaced from the rod's centre of mass, the passing of the wave willresult in some relative motion of the rod and the bead, for in the first approximationthe bead and the mass centre of the rod will each move on a geodesic. This relativemotion will generate heat, and thus locally available energy may be extracted fromthe wave.In these considerations, the effect of the device on the wave has been neglected.This is a test device-a device constructed out of test particles. Consequently, suchconsiderations cannot be used to calculate the total amount of available energy inthe wave.[snip]...............................................................................It is clear from the relative acceleration acquired by test particles, as described in sections 3 and 4, that energyis transferred to test particles by a plane wave, but this does not enable us to makequantitative assertions about energy transport in general. The present fluid stateof the theory of the energy pseudo-tensor would not appear to justify a discussion ofenergy transport in terms of this concept.

I was wondering in your testing did you use a smoke stick also called a smoke pencil to check for air flows around the EM Drive in ambient air conditions?

Although a Google search reveals that this has been brought up before, for example here by @aero: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1275034#msg1275034 there is no entry I could find in the threads as to whether any of the research groups actually used smoke to check air flow. Perhaps others can try separate searches either using their memories or using Google (anything but the poorly functioning "Search" button between "Unread Topics" and "Profile" )

Thank you Rodal for replying, I also couldn't find where this simple test was performed. Maybe it could be something tested at a later date?

Because Peltier effect can't quite reach cryogenic temperatures, for some thermodynamic reason I forgot. Maybe it changed with recent progress on the subject ? Please inquire : what are the limits of low temp. with Peltier effect, now and tomorrow ? Isn't the Peltier effect still quite low in efficiency ?

The Peltier limits are below 100K, which is enough for high-temparature superconductors. The efficiency in such temperature is low, but probably that could be economically viable because of much smaller MW input power and smaller superconducting engine size.

That said, I must sadly admit, that this engine won't probably move in free space. It may move on air cushion though, as in the experiments conducted so far on Earth.

Anyway, if so, then it is at least good for new generation of rotorless helicopters, here on Earth.

Stirling coolers are used where cryogenic temperatures are required. They are more efficient than Peltier devices. I have used very compact Stirling cooled IR detectors. Several companies make them, It takes about 1 Min. to reduce the temperature of the detector to 95 K, using 1 Watt. However the thermal mass is very tiny. NASA has been investigating Stirling coolers for liquifying rocket fuels (H2, O2) in space and for space telescope applications.

Interesting that breaking CofM means that translational invariance dies, and breaking Einstein's SR core principle means that inertial frame invariance dies. Interesting because you may notice that one is essentially the time derivative of the other. And further that breaking CofE means that time invariance dies.

Perhaps that's a deep observation, but I'm not smart enough to know what it means. All I know is that, for a propellantless propulsor, we are forced to choose between killing off one or the other. If we got creative we could kill off both, maybe!

I'm sure my physics friends down the pub here in Cupertino would simply shrug and say that, since momentum appears not be conserved in the first place, there's ample room for odd statements to be correspondingly made about energy conservation (and I have made them here on this forum).

Perhaps there's an exit route out of this bind via playing off conservation of momentum against conservation of energy. Just a wild thought.

The conundrum may be resolved in two words:

Noether's theorem.

In defining how symmetries are enforced, by extension it reveals where they are not.

Specifically, time-dependent (ie. temporally variant) interactions are, by definition, non-conservative. Although we more commonly encounter such asymmetries in dissipative systems, there are, within electromagnetism at least, non-dissipative non-conservative systems.

And before anyone protests, this isn't half as controversial as it may seem - any electrodynamics textbook will include a section on non-conservative, temporally variant EM interactions. By definition, CoE does not and cannot be applied to them. See Rutherford's first paper ca 1886 on magnetic entropy viscosity (Sv)... in such a delayed response, the time-dependent rise of B to a given H means input and output FxD integrals can be non-equitable, if their mechanical displacements are varied to sub- and super-Sv speeds respectively.

Example: take two permanent magnets, at least one of which has appreciable Sv. Allow them to attract together before B can reach Bmax, obtaining our output FxD integral, then let B peak before separating them against this now-higher force, requiring an appropriately-greater input work integral due to the higher force over the same distance.... we've input more work than the interaction has output! Where'd the energy go? Not dissipated to heat (the magnetocaloric profiles are almost identical, and incidental since net change in B up vs down is equal for both integrals - ie. Sv isn't a direct heating mechanism). Rather, the answer's right there in the setup - the missing energy was spent entirely on displacement against a higher magnetic force. Or, looking at it from the alternative perspective, squandered away by not harvesting it in the first place during the initial delayed-response output displacement.

We can repeat this interaction forever, dumping the same amount of mechanical energy into the vacuum (via the virtual photon exchanges mediating the force) each cycle. Calorimetry will show a continuing loss...

And yes, this asymmetry IS reversible, but now things really are getting controversial...

The way to look at it is that time-dependent classical symmetry breaks aren't so much Noether exceptions, as ultimate validations of the principle - an inevitable consequence of passive temporally-variable field densities and their corresponding force magnitudes in non-dissipative systems. The term 'directional vacuum coupler' has already been coined for other RF apparatus, which is a shame as it'd be most apposite here with this unwieldy nomenclature, but i'm no good at neologisms so it is what it is... "temporally-asymmetric non-dissipative systems". These are fundamentally open thermodyanic systems, due to the time-dependence factor, and it is the vacuum that they are open to.

What would make headlines for me would be doing it with momentum... i've been trying for years without success. Mass and momentum always seem to be mediated at C and there's no obvious mechanical equivalents of magnetic properties like coercivity, remanance or permeability etc. I've seen tantalising suggestions, yet nothing concrete, all but concluding that breaking CoE is almost trivial compared to CoM. There's still one or two pots on the boil though, so maybe the EM drive is also a contender.. Might the frustum geometry introduce some kind of temporal variance to the EM interaction between alternate ends of the bell?

Whatever's happening in there, Noether has to have something to say about it....

I was wondering in your testing did you use a smoke stick also called a smoke pencil to check for air flows around the EM Drive in ambient air conditions?

That is a very good idea. I don't think it has been suggested before. There was some discussion on convective air flow and the possiblity it may explain the anomalous force measured by EW early in thread 1. However interest in that explanation has dissipated and Dr. Rodal's analysis of thermal-mechanical effects as a conventional explanation has replaced it.